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課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
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開課學期 |
106-1 |
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授課對象 |
大氣科學系 |
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授課教師 |
劉瓊如 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
08 |
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學分 |
4.0 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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上課時間 |
星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) |
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上課地點 |
新302新302 |
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備註 |
統一教學.大二以上限20人.三10為實習課.
限本系所學生(含輔系、雙修生)
總人數上限：110人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1061MATH1201_08 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions. |
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課程目標 |
Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions. |
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課程要求 |
High School Mathematics |
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預期每週課後學習時數 |
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Office Hours |
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參考書目 |
James Stewart, Calculus Early Transcendentals, 8th edition. (Metric version) |
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指定閱讀 |
待補 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
平常 |
20% |
作業，webwork，小考 |
2. |
期中考 |
40% |
11/4(六) 09:00~11:30 考試範圍 1.4~4.9(英文命題) |
3. |
期末考 |
40% |
1/6(六) 09:00~11:30 考試範圍 5.1~10.6(英文命題) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/13,9/15 |
1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function |
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第2週 |
9/20,9/22 |
2.3
Calculating Limits Using the Limit Laws
2.4
The Precise Definition of a Limit
2.5
Continuity
2.6
Limits at Infinity; Horizontal Asymptotes |
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第3週 |
9/27,9/29 |
2.7
Derivatives and Rates of Change
2.8
The Derivative as a Function
3. Differentiation rules
3.1
Derivatives of Polynomials and Exponential Functions
3.2
The Product and Quotient Rules |
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第4週 |
10/04,10/06 |
10/4 中秋節放假
3.3
Derivatives of Trigonometric Functions
3.4
The Chain Rule |
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第5週 |
10/11,10/13 |
3.5
Implicit Differentiation
3.6
Derivatives of Logarithmic Functions
3.8
Exponential Growth and Decay (✽)
3.9
Related Rates |
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第6週 |
10/18,10/20 |
3.10
Linear Approximations and Differentials
3.11
Hyperbolic Functions
4. Applications of differentiation
4.1
Maximum and Minimum Values
4.2
The Mean Value Theorem |
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第7週 |
10/25,10/27 |
4.3
How Derivatives Affect the Shape of a Graph
4.4
Indeterminate Forms and l''Hospital''s Rule
4.5
Summary of Curve Sketching |
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第8週 |
11/01,11/03 |
4.7
Optimization Problems
4.9
Antiderivatives
緩衝時間 |
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第9週 |
11/08,11/10 |
5.1
Areas and Distances
5.2
The Definite Integral
5.3
The Fundamental Theorem of Calculus
5.4
Indefinite Integrals and the Net Change Theorem
5.5
The Substitution Rule |
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第10週 |
11/15,11/17 |
11/15 校慶停課
6. Applications of integration
6.1
Areas Between Curves
6.2
Volume
6.3
Volumes by Cylindrical Shells |
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第11週 |
11/22,11/24 |
6.5
Average Value of a Function
7. Techniques of integration
7.1
Integration by Parts
7.2
Trigonometric Integrals
7.3
Trigonometric Substitution |
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第12週 |
11/29,12/01 |
7.4
Integration of Rational Functions by Partial Fractions
7.5
Strategy for Integration
7.8
Improper Integrals |
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第13週 |
12/06,12/08 |
8.1
Arc Length
8.2
Area of a Surface of Revolution |
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第14週 |
12/13,12/15 |
8.1
Arc Length
10. Parametric equations and polar coordinates
10.1
Curves Defined by Parametric Equations
10.2
Calculus with Parametric Curves |
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第15週 |
12/20,12/22 |
9.1
Modeling with Differential Equations
9.3
Separable Equations |
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第16週 |
12/27,12/29 |
10.1
Curves Defined by Parametric Equations
10.2
Calculus with Parametric Curves
10.3
Polar Coordinates |
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第17週 |
1/03,1/05 |
10.4
Areas and Lengths in Polar Coordinates |
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